34 citations · 172 across the 30 of their papers we have counts for
5 papers · 1 filter
Continuity points via Riesz potentials for -elliptic operators
Lars Diening, Franz Gmeineder
We establish a Riesz potential criterion for Lebesgue continuity points of functions of bounded -variation, where is a -elliptic differential o…
The Lipschitz truncation of functions of bounded variation
Dominic Breit, Lars Diening, Franz Gmeineder
We construct a Lipschitz truncation which approximates functions of bounded variation in the area-strict metric. The Lipschitz truncation changes the original function only on a sm…
On limiting trace inequalities for vectorial differential operators
Franz Gmeineder, Bogdan Raita, Jean Van Schaftingen
We establish that trace inequalities $$\|D^{k-1}u\|_{L^{\frac{n-s}{n-1}}(\mathbb{R}^{n},dμ)} \leq c \|μ\|_{L^{1,n-s}(\mathbb{R}^{n})}^{\frac{n-1}{n-s}}\|\mathbb{A}[D]u\|_{L^{1}(\ma…
Regularity for higher order quasiconvex problems with linear growth from below
Franz Gmeineder, Jan Kristensen
We announce new existence and -regularity results for minimisers of the relaxation of strongly quasiconvex integrals that on smooth maps $u\colonΩ\subset\mathbb{R}^{n}…
Partial regularity for symmetric quasiconvex functionals on BD
Franz Gmeineder
We establish the first partial regularity results for (strongly) symmetric quasiconvex functionals of linear growth on BD, the space of functions of bounded deformation. By Rindler…